a. For the experiment in which the number of computers in use at a six - computer lab is observed, let B, C be the events defined as B = {3, 4, 5, 6}, and C = {1, 3, 5}. Give the event (B ^ C) using set notation (i.e using { } ).

b. Suppose that the probability of a person getting a certain rare disease is 0.0004 . Consider a town of 10,000 people. What is the approximate probability of seeing more than 3 new cases in a year?

c. To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he will be stopped 10% of work days. During a certain 5 - day work week, what is the probability that he gets stopped at least once during the week?

d. Suppose occurrences of sales on a small company’s website are modeled by a Poisson model with λ = 6/hour. What is the probability that the next sale will happen in the next 12 minutes?

Introduction: In this experiment, the following equilibrium system will be observed:

Fe⁺³_(aq)   +   SCN^-_(aq)   ↔   Fe(SCN)⁺²_(aq)

The reactants are both colorless solutions (the ferric ion is slightly colored, but it is treated with nitric acid to remove the color) while the product has a reddish color. The intensity of the color that is produced is directly proportional to its concentration. If a light source is allowed to shine through such a solution, it is found that the amount of light absorbed (i.e. the energy that is not being transmitted through the solution) is also directly proportional to the concentration of the solution. A spectrophotometer is a device that will shine light through a sample and measure the percent of light that is transmitted and absorbed. These data can be used to determine the equilibrium concentrations in a system by applying Beer’s Law.

            Beer’s Law:   absorbance = ab[colored species]

a = molar absorptivity coefficient of the colored species (constant for a particular wavelength)

b = thickness of the cell used in the measurement

[colored species] = molar concentration.

            Since the same cell will be used throughout the experiment as well as the same wavelength, both a and b will be constants and they will be combined into a single constant labeled Z. Therefore:

                        absorbance = Z[colored species]

Procedure:

A.Preparation of Solutions: Place 6 test tubes in a test tube rack labeled 1-6. Add the reagents listed below using pipettes (pipettes are to be cleaned and prepared in the same manner as a buret). Note that the total volume in each test tube is 20.0 mL.

B.Calibrating the spectrophotometer:

1.Set the wavelength to 447 nm.

2.Rinse a cuvet (small disposable test tube) with distilled water. Fill the cuvet with distilled water and wipe the outside of it with a paper towel to remove any liquid and fingerprints. From this point on, handle the cuvet by the rim only.

3.Insert the cuvet into the sample compartment and press the green calibration button.

C.Determining the Value of Z: The value of Z is determined by measuring the absorbance of a solution of known concentration ( absorbance = Z[colored species] ).   The solution of known concentration was prepared by adding 5.00 mL of .00200 M NaSCN and 25.0 mL of .200M Fe(NO₃)₃ and was diluted to a volume of 100.0 mL. From these quantities it is evident that the ferric nitrate is in extreme excess which forces the equilibrium to the right. It can be assumed that the magnitude of the excess reactant causes the reaction to go to completion. From this information, calculate the concentration of the Fe(SCN)⁺² in the solution. Rinse a cuvet with water and with the solution to be tested. Fill the cuvet with the known concentration solution and insert it into the sample compartment. Record the absorbance value and calculate the value of Z.

D.Determining the Absorbance of the Equilibrium Mixtures: Determine the absorbance for each of the five solutions. Be sure to clean the cuvet each time with distilled water, rinse it with the solution to be tested, and thoroughly wipe the outside of the cuvet.

Data and Calculations:

1. Known Concentration Solution

                        Concentration of Fe(SCN)⁺² : ____________    

                                    show work

Absorbance: 0.424

                        Z: ____________________

                                    show work

            2. Equilibrium Solutions

Given the measured absorbance for test tube 2, show the work for the calculations for each of the concentrations requested in the table above. Record the concentrations for all the test tubes in the table above, but only show the work for test tube 2.

                        [Fe(SCN)+2]

Initial [Fe⁺³]                                            Equilibrium [Fe+3]

Initial [SCN^-]                                          Equilibrium [SCN^-]

Write the expression for K_c for this reaction.

Calculate the value of K_c for each of the five equilibrium mixtures and calculate the average. Show the work for test tube 2 only.

            t.t. 1:   K_c = ____________                t.t. 2:   K_c = ____________

t.t. 3:   K_c = ____________                t.t. 4:   K_c = ____________

t.t. 5:   K_c = ____________                Average K_c =___________

Using 131 as the accepted value for K_c, determine the percent error.

1. An experiment was done to determine if a pair of dice is “fair”, that is, the probability that each number on each die is the same. Tom tosses the dice 50 times and determines that the mean sum of the sample is 6.6, with a standard deviation of 1. 133. According to the mechanics of tossing two dice, the mean should be 7. Determine if this is a fair dice at the .05 level of significance. Also determine the p-value.

1. Determine if a t or a z hypothesis test should be used.
2. Is this a one-tail or a two-tail hypothesis test?
3. Find H0 and H1.
4. Use both the Classical Approach and the P-Value Approach to determine whether to reject or fail to reject the null hypothesis.
5. Interpret the conclusion.

. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model. ∑X = 50 ∑X2 = 200 ∑Y = 75 ∑Y2 = 1600 ∑XY = 400 Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

a. An experiment was performed on a certain metal to determine if the strength is a function of heating time (hours). Results based on 25 metal sheets are given below. Use the simple linear regression model.
∑X = 50
∑X² = 200
∑Y = 75
∑Y² = 1600
∑XY = 400

Find the estimated y intercept and slope. Write the equation of the least squares regression line and explain the coefficients. Estimate Y when X is equal to 4 hours. Also determine the standard error, the Mean Square Error, the coefficient of determination and the coefficient of correlation. Check the relation between correlation coefficient and Coefficient of Determination. Test the significance of the slope.

b. Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primarily on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following (hypothetical) data show the price and overall score for the ten 42-inch plasma televisions (Consumer Report data slightly changed here):

Use the above data to develop and estimated regression equation. Compute Coefficient of Determination and correlation coefficient and show their relation. Interpret the explanatory power of the model. Estimate the overall score for a 42-inch plasma television with a price of $3600 and perform significance test for the slope.

Fremont High School has 2100 students. One of the statistics teachers at the school is interested in whether an intervention program based on self-management improves attendance. They randomly choose 80 students and randomly assign half of them to either an experimental condition (self- management class) or a control condition (distractor class on popular culture). At the end of the semester, they measure the number of days missed for each student. The teacher expects that the students in the self-management class will be absent for fewer days than the control group.

1) What is the population in this experiment?

2) What is the sample in this experiment?

3) What is the response variable in this experiment?

4) If the teacher calculates the average number of absences for the group of 80 students, then that average would be a______. A. Parameter B. Statistic

5) If the teacher calculates the average number of absences from all the 2100 students, then that average would be a_______. A. Parameter B. Statistic

6) The teacher records the number of absences for each student. This record is her______.

Number of absences is a______.

A. data; continuous B. data; discrete

7) Number of absences is a______.

A. Ratio B. Interval C. Nominal D. Ordinal

Problem 3.22. The response time in milliseconds was determined for three different types of circuits that could be used in an automatic valve shutoff mechanism. The results from a completely randomized experiment are shown in the following table:

Circuit Type...........Response Time

a) Test the hypothesis that the three circuit types have the same response time. Use α=0.01.

b) Use Tukey’s test to compare pairs of treatment means. Use α = 0.01.

c) Use the graphical procedure in Section 3.5.3 to compare the treatment means. What conclusions can you draw? How do they compare with the conclusions from part (b)?

d) Construct a set of orthogonal contrasts, assuming that at the outset of the experiment you suspected the response time of circuit type 2 to be different from the other two.

e) If you were the design engineer and you wished to minimize the response time, which circuit type would you select?

f) Analyze the residuals from this experiment. Are the basic analysis of variance assumptions satisfied?

PLEASE MAKE SURE IS A "MINITAB" ANSWER, OTHERWISE... DON'T BOTHER. THANK YOU.

A company that stamps gaskets out of cork sheets and wants to compare the mean number of gaskets produced per hour for three different types of stamping machines. The company wants to use the data to determine whether one machine is more productive than the other. To answer these questions, the manufacturer decides to conduct an experiment with each of the machines operating for six 1-hour time periods assigned in a random order to eliminate the possibility of bias. The data for the experiment, the number of gaskets (in thousands) produced per hour is shown below. (a) State the hypotheses and conduct an analysis of variance at α = 0.05 to test the hypotheses. Create a boxplots of the data as part of the oneway ANOVA. (b) Plot and analyze the residuals from the experiment and comment on model adequacy. (c) Is there sufficient evidence to indicate that any machine is more productive than the others? Machine 1 Machine 2 Machine 3 431 427 440 436 442 448 401 394 389 404 441 418 421 409 418 425 393 422